Abundant closed-form solitary solutions of a nonlinear neurobiological model for analyzing numerous signal transmission behaviors through the neuron using recent scheme

Abstract This study is to construct the solitary wave solutions to the nonlinear Fitzhugh-Nagumo (FN) model. The Fitzhugh-Nagumo(FN) model is a simplification form of the Hodgkin-Huxley model for nerve's impulse transmission through the nerve fibers, it also described the noise formations in circuit theory, the intercellular trigger waves and more. This is indubitably very important mathematical model in various neurobiological sciences and engineering applications. The generalized exponential rational function (GERF) technique is imposed to the considered model which accumulates different wave solutions in suitable form. In addition, we analyze the effects of wave velocity on the attained solutions, to realize the dynamical behavior of the related phenomenon. The attained results confirm the efficiency and consistency of the considered technique.